Thermalization of the lower polaritons may occur due to different physical processes depending on the system.
For example, in organic polariton systems, thermalization occurs due to their nonlinear interaction with low frequency vibrations [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
For polariton states in inorganic semiconductors thermalization predominantly goes through interactions with acoustic phonons or free charges [8]}.
The thermalization of the polaritons can also occur due to polariton–polariton scattering [9]}, [10]}.
However, regardless of the mechanism, the thermalization can be described through the Lindblad superoperator [8]}, [12]}.
\({L_{{\rm {therm}}}}\left( {\hat{\rho }} \right) = \sum _{\bf k} \sum _{{\bf q}\ne {\bf k}} {\Gamma _{\bf kq}}\times \\{\left( {{{\hat{a}}_{\bf k}}\hat{a}_{\bf q}^\dag \hat{\rho }{{\hat{a}}_{\bf q}}\hat{a}_{\bf k}^\dag - \frac{1}{2}\hat{\rho }{{\hat{a}}_{\bf q}}\hat{a}_{\bf k}^\dag {{\hat{a}}_{\bf k}}\hat{a}_{\bf q}^\dag - \frac{1}{2}{{\hat{a}}_{\bf q}}\hat{a}_{\bf k}^\dag {{\hat{a}}_{\bf k}}\hat{a}_{\bf q}^\dag \hat{\rho }} \right)} ,\) 
